Open AccessLocally asymptotically rank-based procedures for testing autoregressive moving average dependence
Author(s) -
Marc Hallin,
Madan L. Puri
Publication year - 1988
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.85.7.2031
Subject(s) - mathematics , statistic , rank (graph theory) , asymptotically optimal algorithm , autoregressive–moving average model , autoregressive model , test statistic , minimax , asymptotic distribution , statistics , white noise , autocorrelation , statistical hypothesis testing , mathematical optimization , combinatorics , estimator
The problem of testing a given autoregressive moving average (ARMA) model (in which the density of the generating white noise is unspecified) against other ARMA models is considered. A distribution-free asymptotically most powerful test, based on a generalized linear serial rank statistic, is provided against contiguous ARMA alternatives with specified coefficients. In the case in which the ARMA model in the alternative has unspecified coefficients, the asymptotic sufficiency (in the sense of Hájek) of a finite-dimensional vector of rank statistics is established. This asymptotic sufficiency is used to derive an asymptotically maximin most powerful test, based on a generalized quadratic serial rank statistic. The asymptotically maximin optimal test statistic can be interpreted as a rank-based, weighted version of the classical Box-Pierce portmanteau statistic, to which it reduces, in some particular problems, under gaussian assumptions.